Colacunary sequences in L-spaces
Combinatorial inequalities and subspaces of L₁
Let M₁ and M₂ be N-functions. We establish some combinatorial inequalities and show that the product spaces are uniformly isomorphic to subspaces of L₁ if M₁ and M₂ are “separated” by a function , 1 < r < 2.
Commutative, radical amenable Banach algebras
There has been a considerable search for radical, amenable Banach algebras. Noncommutative examples were finally found by Volker Runde [R]; here we present the first commutative examples. Centrally placed within the construction, the reader may be pleased to notice a reprise of the undergraduate argument that shows that a normed space with totally bounded unit ball is finite-dimensional; we use the same idea (approximate the norm 1 vector x within distance η by a “good” vector ; then approximate...
Compacidad débil en espacios de funciones integrables-Bochner, y la propiedad de Radon-Nikodym.
Compactness and countable compactness in weak topologies
A bounded closed convex set K in a Banach space X is said to have quasi-normal structure if each bounded closed convex subset H of K for which diam(H) > 0 contains a point u for which ∥u-x∥ < diam(H) for each x ∈ H. It is shown that if the convex sets on the unit sphere in X satisfy this condition (which is much weaker than the assumption that convex sets on the unit sphere are separable), then relative to various weak topologies, the unit ball in X is compact whenever it is countably compact....
Complemented and uncomplemented subspaces of Banach spaces.
Does a given Banach space have any non-trivial complemented subspaces? Usually, the answer is: yes, quite a lot. Sometimes the answer is: no, none at all.
Complemented copies of c0 in vector-valued Köthe-Dieudonné function spaces.
Let [Lambda] be a barrelled perfect (in the sense of J. Dieudonné) Köthe space of measurable functions defined on an atomless finite Radon measure space. Let X be a Banach space containing a copy of c0, then the space [Lambda(X)] of [Lambda]-Bochner integrable functions contains a complemented copy of c0.
Complemented copies of spaces in tensor products
We give sufficient conditions on Banach spaces and so that their projective tensor product , their injective tensor product , or the dual contain complemented copies of .
Complemented subspaces of -adic second dual Banach spaces.
Complemented subspaces of sums and products of copies of L1[0, 1].
We prove that the direct sum and the product of countably many copies of L1[0, 1] are primary locally convex spaces. We also give some related results.
Completely continuous multilinear operators on C(K)-spaces.
The purpose of this note is to announce, without proofs, some results concerning vector valued multilinear operators on a product of C(K) spaces.
Completely Continuous operators
A Banach space X has the Dunford-Pettis property (DPP) provided that every weakly compact operator T from X to any Banach space Y is completely continuous (or a Dunford-Pettis operator). It is known that X has the DPP if and only if every weakly null sequence in X is a Dunford-Pettis subset of X. In this paper we give equivalent characterizations of Banach spaces X such that every weakly Cauchy sequence in X is a limited subset of X. We prove that every operator T: X → c₀ is completely continuous...
Complex Strict Convexity of Certain Banach Spaces.
Composition results for strongly summing and dominated multilinear operators
In this paper we prove some composition results for strongly summing and dominated operators. As an application we give necessary and sufficient conditions for a multilinear tensor product of multilinear operators to be strongly summing or dominated. Moreover, we show the failure of some possible n-linear versions of Grothendieck’s composition theorem in the case n ≥ 2 and give a new example of a 1-dominated, hence strongly 1-summing bilinear operator which is not weakly compact.
Compound invariants and embeddings of Cartesian products
New compound geometric invariants are constructed in order to characterize complemented embeddings of Cartesian products of power series spaces. Bessaga's conjecture is proved for the same class of spaces.
Containing l1 or c0 and best approximation.
The purpose of this paper is to obtain sufficient conditions, for a Banach space X to contain or exclude c0 or l1, in terms of the sets of best approximants in X for the elements in the bidual space.
Continuous and generalized solutions of singular partial differential equations.
Continuous restrictions of linear functionals
Copies of C0 in Certain Vector-Valued Function Banach Spaces.
Copies of and in Musielak-Orlicz sequence spaces
Criteria in order that a Musielak-Orlicz sequence space contains an isomorphic as well as an isomorphically isometric copy of are given. Moreover, it is proved that if , where are defined on a Banach space, does not satisfy the -condition, then the Musielak-Orlicz sequence space of -valued sequences contains an almost isometric copy of . In the case of it is proved also that if contains an isomorphic copy of , then does not satisfy the -condition. These results extend some...